Practical Applications of The Free Boundary of the American Put

Abstract

Has one of the most vexing problems of mathematical finance been solved? In The Free Boundary of the American Put, from the Winter 2020 issue of The Journal of Derivatives, author Thomas Little (of Hard Analytics in Houston) says he has done exactly that, presenting an analytic formula to determine the early expiry boundary curve for American put options more quickly and accurately than has been possible in the past. Unlike European-style put options, which may be exercised only on or near their expiration dates, American puts may be exercised at any time prior to expiration. Most American puts are, in fact, held until expiration, but traders may exercise a put early for any of a number of reasons. If the early expiry boundary curve could be accurately calculated, thus determining the critical asset price at or below which a put should be exercised to avoid arbitrage, traders could more confidently make early expiry decisions and time their trades. Little says that his formula provides that curve accurately along the full time line of the option. The next step will be to back test a portfolio of American put options during several market cycles to see whether the use of Little’s formula would have produced better outcomes than those achieved with current practices. TOPICS: Options, fundamental equity analysis, statistical methods